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Sunday, August 22, 2010

GeoGebra... times 3!

I made a GeoGebra spirals applet -- for use in my Precalc class! Yay. I'll be introducing geometric and arithmetic sequences sometime during the next week, and even though we'll spend most of that period working on finding numeric trends embedded in composite patterns and such, I think that at the end of class, I am going to use the applet to help them appreciate the connection between nature and geometric sequences. :)

Anyway, that's enough preamble; check it out for yourself! You can make a spiral outwards (if geometricRatio > 1) or inwards (if geometricRatio < 1), and I'll ask the kids to make predictions about what they will see with those ratios before we toggle the numbers. You can also turn on Trace for point B in order to see the actual spirally points.

Amazingly, that's three times in one week that I'll be using GeoGebra. (First time I'll be showing my Geometry kids briefly what Mr. H created per my request, so that they can better visualize why 3 points will define a plane in space. The second time, I'll be taking my Geometry kids down to the computer lab to do a full period of GeoGebra exploration in pairs about Segment Addition Postulate and the midpoint of a segment. See worksheet below if you are interested in seeing just how explicitly I structure an activity like this for 9th-graders who've never seen any geometry software before. If you want the actual file, drop me a note. I did all the way up through step #15 with my 9th-graders from last year and they had all loved it, so I am interested to see if the more challenging parts I tagged on this year will end up "breaking" it. --I guess we will see!)

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Also this week, I'm pulling out an old middle-school activity that I liked a lot, in introducing angles and the estimation of angles. I found out on Friday (during the beginning of our tangrams project) that a handful of my kids didn't know how to recognize right angles in a diagram. Some of the same kids also didn't know that when one angle is 90 degrees (at what looks like a perpendicular intersection), its adjacent angles would also be 90 degrees. ...I have to say, that's pretty alarming. So, umm, we're starting from the basics.

The activity is one that I've done with middle-schoolers many times. You give kids each a piece of patty paper, and you get them to fold it several times and to cut an arc so that when they open it back up, they have a circle that has creases across every 22.5 degrees. Then you just start calling out angles that are multiples of 22.5 degrees, and kids have to figure out (without a protractor) how to use their patty paper to show 90 degrees, 45 degrees, 180 degrees, 135 degrees (at which point, they would have to put it together with someone else's angle), 67.5 degrees, etc. Essentially, the kids learn to estimate angle sizes by comparing them against benchmark angles and thinking about fractions of 90 degrees. (You could also use this manipulative to discuss why when you compare two angles, the sizes of their rays don't matter.)